We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are l...We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.展开更多
Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for ...Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.展开更多
At low-Reynolds-number,the performance of airfoil is known to be greatly affected by the formation and burst of a laminar separation bubble(LSB),which requires a more precise simulation of the delicate flow structures...At low-Reynolds-number,the performance of airfoil is known to be greatly affected by the formation and burst of a laminar separation bubble(LSB),which requires a more precise simulation of the delicate flow structures.A framework based on the interior penalty discontinuous Galerkin method and large eddy simulation approach was adopted in the present study.The performances of various subgrid models,including the Smagorinsky(SM)model,the dynamic Smagorinsky(DSM)model,the wall-adapting local-eddy-viscosity(WALE)model,and the VREMAN model,have been analyzed through flow simulations of the SD7003 airfoil at a Reynolds number of 60000.It turns out that the SM model fails to predict the emergence of LSB,even modified by the Van-Driest damping function.On the contrary,the best agreement is generally achieved by the WALE model in terms of flow separation,reattachment,and transition locations,together with the aerodynamic loads.Furthermore,the influence of numerical dissipation has also been discussed through the comparison of skin friction and resolved Reynolds stresses.As numerical dissipation decreases,the prediction accuracy of the WALE model degrades.Meanwhile,nonlinear variation could be observed from the performances of the DSM model,which could be attributed to the interaction between the numerical dissipation and the subgrid model.展开更多
The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional ...This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.展开更多
In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem....In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.展开更多
We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem...We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem using Kuhn-Tucker optimality condition and discuss the relations between them. Finally, two examples are used to illustrate the feasibility of the proposed penalty method.展开更多
In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with...In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.展开更多
The electromagnetic detection satellite （EDS） is a type of earth observation satellites （EOSs）. The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The...The electromagnetic detection satellite （EDS） is a type of earth observation satellites （EOSs）. The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm （GA） is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm.展开更多
By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method...By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametdc hybrid finite element was discussed. The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.展开更多
We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was ...We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.展开更多
In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an i...In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.展开更多
Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand...Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods.展开更多
A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order...A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.展开更多
Aimed at the great computing complexity of optimal brain surgeon (OBS) process, a pruning algorithm with penalty OBS process is presented. Compared with sensitive and regularized methods, the penalty OBS algorithm not...Aimed at the great computing complexity of optimal brain surgeon (OBS) process, a pruning algorithm with penalty OBS process is presented. Compared with sensitive and regularized methods, the penalty OBS algorithm not only avoids time-consuming defect and low pruning efficiency in OBS process, but also keeps higher generalization and pruning accuracy than Levenberg-Marquardt method.展开更多
The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.展开更多
A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size ...A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size h satisfy H=O(h 13-s )(s=0(n=2);s=12(n=3), where n is a space dimension), this method has the same convergence accuracy as the usual finite element method. But the two grid method can save a lot of computation time for its brief calculation. Moreover, a numerical test was couducted in order to verify the correctness of above theoretical analysis.展开更多
In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an al...In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.展开更多
The penalty function method of continuum shape optimization and its sensitivity analysis technique are presented. A relatively simple integrated shape optimization system is developed and used to optimize the design o...The penalty function method of continuum shape optimization and its sensitivity analysis technique are presented. A relatively simple integrated shape optimization system is developed and used to optimize the design of the inner frame shape of a three-axis test table. The result shows that the method converges well, and the system is stable and reliable.展开更多
This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces,implemented by the constant-strain assumed enhanced strain(AES)method,where penalty method is used t...This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces,implemented by the constant-strain assumed enhanced strain(AES)method,where penalty method is used to impose both non-penetration constraint and Coulomb’s law of friction.The proposed constant-strain AES method for modeling embedded frictional contact can be cast into an integration algorithm similar to those used in the classical plasticity theory,where displacement jump is calculated from the local traction equilibrium at Gauss point,so the method does not introduce any additional global degrees of freedom.Moreover,constant-strain elements are often desirable in practice because they can be easily created automatically for large-scale engineering applications with complicated geometries.As encountered in other enriched finite element methods for frictional contact,the problem of normal contact pressure oscillations is also observed in the constant-strain AES method.Therefore,we developed a strain-smoothing procedure to effectively mitigate the oscillations.We investigated and verified the proposed AES framework through several numerical examples,and illustrated the capability of this method in solving challenging nonlinear frictional contact problems.展开更多
文摘We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.
基金supported in part by the National Natural Science Foundation of China(62276119)the Natural Science Foundation of Jiangsu Province(BK20241764)the Postgraduate Research & Practice Innovation Program of Jiangsu Province(KYCX22_2860)
文摘Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.
基金This work was supported by the National Key R&D Program of China(Grant No.2022YFE0207000)the National Natural Science Foundation of China(Grant Nos.12372289,11972250,and 12102298)+1 种基金the China Postdoctoral Science Foundation(Grant No.2021M702443)Tianjin Natural Science Foundation(Grant No.22JCZDJC00910).
文摘At low-Reynolds-number,the performance of airfoil is known to be greatly affected by the formation and burst of a laminar separation bubble(LSB),which requires a more precise simulation of the delicate flow structures.A framework based on the interior penalty discontinuous Galerkin method and large eddy simulation approach was adopted in the present study.The performances of various subgrid models,including the Smagorinsky(SM)model,the dynamic Smagorinsky(DSM)model,the wall-adapting local-eddy-viscosity(WALE)model,and the VREMAN model,have been analyzed through flow simulations of the SD7003 airfoil at a Reynolds number of 60000.It turns out that the SM model fails to predict the emergence of LSB,even modified by the Van-Driest damping function.On the contrary,the best agreement is generally achieved by the WALE model in terms of flow separation,reattachment,and transition locations,together with the aerodynamic loads.Furthermore,the influence of numerical dissipation has also been discussed through the comparison of skin friction and resolved Reynolds stresses.As numerical dissipation decreases,the prediction accuracy of the WALE model degrades.Meanwhile,nonlinear variation could be observed from the performances of the DSM model,which could be attributed to the interaction between the numerical dissipation and the subgrid model.
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
文摘This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.
文摘In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.
基金Supported by the National Natural Science Foundation of China(11501233)the Key Project of Anhui Province University Excellent Youth Support Plan(gxyqZD2016102)
文摘We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem using Kuhn-Tucker optimality condition and discuss the relations between them. Finally, two examples are used to illustrate the feasibility of the proposed penalty method.
基金Supported by the Key Project on Science and Technology of Hubei Provincial Department of Education (D20103001)
文摘In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.
基金supported by the National Natural Science Foundation of China(6110118461174159)
文摘The electromagnetic detection satellite （EDS） is a type of earth observation satellites （EOSs）. The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm （GA） is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm.
文摘By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametdc hybrid finite element was discussed. The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.
基金supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement(823731CONMECH)supported by National Natural Science Foundation of China(11671101),supported by National Natural Science Foundation of China(11961074)+2 种基金Guangxi Natural Science Foundation(2021GXNSFAA075022)Project of Guangxi Education Department(2020KY16017)Yulin normal university of scientific research fund for high-level talents(G2019ZK39,G2021ZK06)。
文摘We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.
基金supported by National Natural Science Foundation of China(72031009 and 71871171)the National Social Science Foundation of China(20&ZD058).
文摘In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.
基金Supported by the National Natural Science Foundation of China (10791203, 11271340)the Natural Science Foundation of Henan Province (112300410109)
文摘Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods.
文摘A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.
文摘Aimed at the great computing complexity of optimal brain surgeon (OBS) process, a pruning algorithm with penalty OBS process is presented. Compared with sensitive and regularized methods, the penalty OBS algorithm not only avoids time-consuming defect and low pruning efficiency in OBS process, but also keeps higher generalization and pruning accuracy than Levenberg-Marquardt method.
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.
文摘A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size h satisfy H=O(h 13-s )(s=0(n=2);s=12(n=3), where n is a space dimension), this method has the same convergence accuracy as the usual finite element method. But the two grid method can save a lot of computation time for its brief calculation. Moreover, a numerical test was couducted in order to verify the correctness of above theoretical analysis.
文摘In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.
文摘The penalty function method of continuum shape optimization and its sensitivity analysis technique are presented. A relatively simple integrated shape optimization system is developed and used to optimize the design of the inner frame shape of a three-axis test table. The result shows that the method converges well, and the system is stable and reliable.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No.2021FZZX001-14)and ZJU-ZCCC Institute of Collaborative Innovation (Grant No.ZDJG2021005).
文摘This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces,implemented by the constant-strain assumed enhanced strain(AES)method,where penalty method is used to impose both non-penetration constraint and Coulomb’s law of friction.The proposed constant-strain AES method for modeling embedded frictional contact can be cast into an integration algorithm similar to those used in the classical plasticity theory,where displacement jump is calculated from the local traction equilibrium at Gauss point,so the method does not introduce any additional global degrees of freedom.Moreover,constant-strain elements are often desirable in practice because they can be easily created automatically for large-scale engineering applications with complicated geometries.As encountered in other enriched finite element methods for frictional contact,the problem of normal contact pressure oscillations is also observed in the constant-strain AES method.Therefore,we developed a strain-smoothing procedure to effectively mitigate the oscillations.We investigated and verified the proposed AES framework through several numerical examples,and illustrated the capability of this method in solving challenging nonlinear frictional contact problems.
